{"paper":{"title":"On growing connected beta-skeletons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cs.CG","authors_text":"Andrew Adamatzky","submitted_at":"2013-04-07T11:58:28Z","abstract_excerpt":"A $\\beta$-skeleton, $\\beta \\geq 1$, is a planar proximity undirected graph of an Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set. Parameter $\\beta$ determines the size and shape of the lune-based neighbourhood. A $\\beta$-skeleton of a random planar set is usually a disconnected graph for $\\beta>2$. With the increase of $\\beta$, the number of edges in the $\\beta$-skeleton of a random graph decreases. We show how to grow stable $\\beta$-skeletons, which are connected for any given value of $\\beta$ and character"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}